We look at the division of 578234 by 6 
We want to divide 578234 by 6.

Going ahead to step 1:
6 can be fit into 5 0 times, resulting in a remainder of 5.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Take the next digit (7) from the dividend and append it to 5, then repeat: 57 / 6

Moving on to step 2:
6 can be fit into 57 9 times, resulting in a remainder of 3.
Use 9 as the next digit of our solution. 
Result so far: 9.0
The remainder is 3 after subtracting 54 from 57.
Include the next digit (8) from the dividend after 3, then repeat: 38 / 6

Going ahead to step 3:
6 goes into 38 6 times with a remainder of 2.
The number 6 becomes the next digit in our result. 
Result so far: 96.0
Deduct 36 from 38 and we're left with 2.
Take the next digit (2) from the dividend and append it to 2, then repeat: 22 / 6

Let's proceed to step 4:
6 can be fit into 22 3 times, resulting in a remainder of 4.
Record the quotient 3 as the next digit in the result. 
Result so far: 963.0
Subtract 18 from 22 to get 4.
Bring next digit (3) of the dividend behind the 4 and repeat the process: 43 / 6

Let's proceed to step 5:
6 can be fit into 43 7 times, resulting in a remainder of 1.
Write down 7 as next digit of the result. 
Result so far: 9637.0
Deduct 42 from 43 and we're left with 1.
Include the next digit (4) from the dividend after 1, then repeat: 14 / 6

Step 6:
If we divide 14 by 6, we get 2 and a remainder of 2.
The number 2 becomes the next digit in our result. 
Result so far: 96372.0
The remainder is 2 after subtracting 12 from 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Advancing to step 7:
6 goes into 20 3 times with a remainder of 2.
The next digit of our result is 3. 
Result so far: 96372.3
If we subtract 18 from 20, we get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

On to step 8:
6 can be fit into 20 3 times, resulting in a remainder of 2.
The next digit of our result is 3. 
Result so far: 96372.33
Subtracting 18 from 20 leaves us with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

After the division, we end up with 96372.33 and a remainder of 0.002.